Homework Assignment 7: (1) Let f(x) be the probability density function of the Pareto random variable; that is, f(x) = αθ α / (x+ θ ) α + 1 , α > 0, θ > 0,x > 0. Show that F(x) = 1 – [ θ / (x + θ )] α and λ (x) = α / (x + θ ). (2) Use the hazard rate function to show that the Weibull distribution is light tailed when α > 1. (Ans λ (x) = αλ x α-1 . Since the hazard rate function is increasing when α > 1, the distribution will have a light tail.) (3) An automobile collision insurance policy reimburses repair costs subject to a deductible of 250 per accident. In the event of an accident, repair costs can be modeled by a uniform random variable on the interval (0,1500). (a) Determine the expected value of the claim payment per loss random variable . (Ans 520.83) (b) Determine the expected value of the claim payment per payment random variable. (Ans 625) (c) Determine the expected value of the claim payment per payment random variable if the deductible is eliminated. (Ans 750)
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Probability theory, insurance company, Weibull, 13.85%, 13.85 %